One plot idea could be Percy emerging from a battle with a water monster, dripping wet and having to find shelter in an unexpected place, like a hidden cave that has some ancient prophecy written on the walls. Another could be Percy getting drenched during a wild storm at Camp Half - Blood and then discovering a new power related to water while in that dripping wet state. Maybe he's dripping wet after being pushed into a magical pool and when he comes out, he can communicate with sea creatures in a new way.
A possible plot for a Percy Jackson dripping wet fanfic could be that Percy is sent on a mission to retrieve a powerful water - based artifact. When he finally reaches the location of the artifact, it is guarded by a series of water traps. He gets through them but ends up dripping wet. While wet, he realizes that the artifact has a connection to his past, something he didn't know before. As he tries to make his way back to camp, he has to face some challenges because of his wet state, like his clothes weighing him down and his shoes making squelching noises. But he also discovers that being wet gives him an advantage in some situations, like being able to blend in with water - based illusions more easily.
One way to vividly describe Percy's dripping wet state is to focus on the sensations. Percy would feel the cold water seeping through his clothes, making him shiver slightly. His skin would be slick with water, and the air around him would feel damp. The author could describe the water as trickling down his back, like cold fingers tracing his spine. His hair would be a tangled mess of wet strands, and when he shakes his head, droplets of water fly in all directions. The wet fabric of his clothes would be chafing against his skin, and he would be constantly aware of the water dripping from his elbows and knees. This detailed description of the physical sensations would bring his dripping wet state to life for the readers.
One idea could be that your inserted character is a new camper who has a special ability related to an ancient and forgotten Greek magic. This character then helps Percy and his friends in a battle against a revived mythological villain that is more powerful than any they've faced before.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
Well, you could have a fanfic where Percy is given a science homework about marine biology, and he uses his knowledge from being the son of Poseidon to write an amazing paper. He might even bring in some sea creatures from the ocean to show as examples, which of course causes chaos in the classroom. Another idea is that the whole demigod gang has to do a group project on mythology, and they each contribute their own unique experiences with the gods and monsters.
In a 'Percy Jackson tattoo fanfic', you could explore the idea of a tattoo artist who is actually a minor god or goddess. The story could follow Percy or another character as they go to get a tattoo from this divine artist. The tattoo could have powers that are both a blessing and a curse, like it gives the wearer enhanced strength but also attracts more monsters. And the process of getting the tattoo could be filled with mythological elements, like the ink being made from the essence of a magical creature.
One idea could be a story where Percy and Phoebe team up to face a new threat that neither of them could handle alone. Maybe it's a powerful monster that has the ability to control water and fire, so Percy's water powers and Phoebe's skills need to be combined.
One idea could be a fanfic where Percy has a dream that he's in an alternate version of Camp Half - Blood. In this dream, the cabins are arranged differently, and there are new campers with strange powers. Another idea is a dream where Percy dreams of his future, seeing himself as a teacher at Camp Half - Blood, passing on his knowledge and skills to the new generation of demigods. Or perhaps a fanfic where Percy has a recurring dream about an ancient prophecy that he has to figure out in his waking life.
Another concept could be a Phoenix being reborn as a human - like form and becoming Percy's ally. They team up to fight against a new threat that neither could face alone. The Phoenix - human hybrid could have special powers that combine the best of both worlds, and their friendship could be a central theme in the fanfic.
In a Percy Jackson Tartarus fanfic, a great plot could be centered around Tartarus corrupting the very essence of Percy's powers. He starts to lose control of his water - based abilities and instead they become tainted with the darkness of Tartarus. Percy then has to go on a journey within Tartarus to find a way to cleanse his powers, all while being hunted by the most dangerous creatures that lurk in the abyss.
A really interesting plot would be if Percy lost his memory and ended up in a mortal town. He has to figure out who he is on his own while still being hunted by some old enemies. The gods are aware of his situation but can't interfere directly because of some ancient rule. So Percy has to rely on his instincts and any small clues he can find about his past to get back to his normal self and his life at Camp Half - Blood.